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maw [93]
3 years ago
13

The diagram shows a right-angled triangle.

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
7 0

Answer:

h = 9.87 cm

Step-by-step explanation:

Given that,

Base, b = 8 cm

Height = h

Angle, \theta=51^{\circ}

We need to find the value of h. We can use trigonometry to find h.

\tan\theta=\dfrac{\text{Perpendicular}}{\text{Base}}\\\\\tan(51)=\dfrac{h}{8}\\\\h=\tan(51)\times 8\\\\h=9.87\ cm

So, the height of the triangle is 9.87 cm.

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One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroi
lukranit [14]

Answer:

1) Random: A random sample needs to be obtained in order to apply inference for the mean

2) Normality condition: The sampling distribution of \bar X needs to be approximately normal. If we use a random sample size higher than 30 we can use the Central Limit theorem to verify this condition.

3) Independence: All the individual observations need to be independent. And we need to satisfy that our sample would be lower than 10% of the real population size.

Step-by-step explanation:

For this case we need three conditions:

1) Random: A random sample needs to be obtained in order to apply inference for the mean

2) Normality condition: The sampling distribution of \bar X needs to be approximately normal. If we use a random sample size higher than 30 we can use the Central Limit theorem to verify this condition.

3) Independence: All the individual observations need to be independent. And we need to satisfy that our sample would be lower than 10% of the real population size.

Data given and notation  

\bar X=203 represent the sample mean

s=10.9 represent the sample standard deviation  

n=17 sample size  

\mu_o represent the value that we want to test  

\alpha=0.01 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We can assume the following system of hypothesis.

Null hypothesis:  \mu = \mu_o  

Alternative hypothesis :\mu\neq \mu_o  

The degrees of freedom on this case:

df=n-1=10-1

Compute the test statistic

The statistic for this case is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

7 0
3 years ago
In 2–4, write Yes or No to indicate whether the expressions are equivalent. 2. 10x - 3 + 2x - 5 and 4(3x - 2) 3. 3y + 3 and 9(y
Dmitry [639]

Step-by-step explanation:

2. 10x - 3 + 2x - 5 and 4(3x - 2)

10x - 3 + 2x - 5

Upon simplifying;

10x + 2x - 3 - 5

12x - 8

4(3x - 2)

12x - 8

Both expressions are equivalent - Yes!

3. 3y + 3 and 9(y + 1/3)

9(y + 1/3)

upon simplifying;

9y + 9 (1/3)

9y + 3

3y + 3

Both expressions are not equivalent - No!

4. 6(3x + 1) and 9x + 6 + 9x

6(3x + 1)

upon simplifying;

6(3x) + 6 (1)

18x + 6

9x + 6 + 9x

Upon simplifying;

9x + 9x + 6

18x + 6

Both expressions are equivalent - Yes!

3 0
3 years ago
H. 7 ones 2 tenths + 4 tenths =<br> tenths =
nlexa [21]

Answer:

67

Step-by-step explanation:

7 ones are just 7, 2 tenths and 4 tenths are 20 and 40. If you add 7 + 40 + 20, you will get 67.

4 0
2 years ago
Read 2 more answers
Sam made 2/3 liter of punch and 3/4 liter of tea to take to a party. How many liters of bervages did sam bring to the party?
JulsSmile [24]
First, what you have to do, is make like denominators of 2/3 and 3/4.

That leaves you with 8/12 and 9/12.

Now, you add those up to get 17/12.

Your answer as a mixed number: 1 5/12
Your answer as a an improper fraction: 17/12
Your answer as a decimal: 1.4166666....

Hope this Helps!

~JaredEkey
4 0
2 years ago
Read 2 more answers
2.4-(1.2)+6.3+(-4.1)-7.3
dybincka [34]

Answer:

-3.9

Step-by-step explanation:

4 0
3 years ago
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